Cutting is such a personal matter, is this something you feel that you should share with him? If this is a relationship based on friendship and trust then maybe sharing this with him would be beneficial for you. Since he is battling depression himself he may be a very understanding confidant.

Thinking you are a "bother" to him doesn't sound like a safe emotional environment for you to share something to deep though, so make sure that you're doing it for the right reasons - and be prepared to answer questions and share more of yourself with this person.

If he's worth it in your eyes, by all means open up emotionally - it's a good thing to do when you're feeling conflicted like this. If you feel more doubt however, maybe just hold off until you feel more comfortable sharing.